In our city there are more and more cars and buses on the roads. Many people drive to work .First, it's good to have a car. You needn't to wait for the bus. You can go to work on time. Then ,there are many busy roads in the city . Can you drive safely? Traffic lights are very important. You must look at the traffic lights and wait for the green man. If someone is crossing the road, you must stop your car and look carefully. We must follow the rules and stay safe on the road.

$\begin{array}{c}\frac{a_1+a_2}{2}\ge \sqrt{a_1{a}_2}\\ \frac{a_1+a_2+a_3}{3}\ge \sqrt[3]{a_1{a}_2{a}_3}\\ \frac{a_1+a_2+a_3+a_4}{4}\ge \sqrt[4]{a_1{a}_2{a}_3{a}_4}\\ \cdots \cdots \cdots \end{array}$  

照此规律，当 $n\in N^{+}\left(n\ge 2\right)$  时， $\frac{a_1+a_2+a_3+\cdots +a_n}{n}\ge$ ____．

如图所示，有一根长L₁=0.5m的木棍，悬挂在某房顶上，木棍的上端与窗台上沿的竖直距离h=4.55m，窗口高为L₂=1.5m．某时刻木棍脱落，不计空气阻力，g取10m/s²．求：